Statistics textbooks covering moments/cumulants

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Discussion Overview

The discussion centers on finding suitable textbooks that cover the concepts of moments and cumulants in statistics, particularly in the context of time series analysis. Participants share their experiences and suggest resources to help someone with a PhD-level engineering background enhance their understanding of these statistical tools.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant expresses a need for resources on moments and cumulants due to a lack of coverage in their undergraduate statistics course.
  • Another participant suggests "The Advanced Theory of Statistics Vol1" by Kendall and Stewart, noting it may be challenging for beginners.
  • A different participant recommends "Probability, Random Variables and Stochastic Processes" by Athanasios Papoulis as a standard text for engineers.
  • Another participant mentions familiarity with "Random Data" by Bendat and Piersol as a relevant resource.

Areas of Agreement / Disagreement

Participants generally agree on the need for resources but suggest different texts, indicating multiple competing views on the best starting point for learning about moments and cumulants.

Contextual Notes

Some suggestions may depend on prior knowledge of random processes, which could affect the accessibility of the recommended texts.

boneh3ad
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I've been looking into time series analysis from a statistical perspective (looking to expand my bag of tools in analyzing experimental data) and I repeatedly run into the concept of moment and cumulant spectra. The problem is that my undergraduate course on statistics back in the day essentially never covered cumulants and only barely touched moments, and so my background is insufficient to grasp some of the richer texts on this subject.

Does anyone have any suggested resources/texts that cover this topic?

FWIW, my background is PhD-level engineering.
 
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Kendall and Stewart's The Advanced Theory of Statistics Vol1 comes to mind but it might be a difficult place to start. Have you any experience with Random Processes? If not, I'd suggest Random Signals by Shanmugan and Breiphol.
 
If you are an engineer, then the following book is the standard:
Probability, Random Variables and Stochastic Processes by Athanasios Papoulis.
 
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I have a little bit of familiarity with the topic based on experiences with Random Data by Bendat and Piersol.
 

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